Population Estimation Procedures
Absolute versus Relative Density
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Absolute Versus Relative Density
Catch Per Unit Effort
Nearest Neighbour Estimates
Transect Sampling
Hayne’s Estimator
Line Transect Estimators
Sightability Models
Mark-Recapture Techniques
Examples of combined applications
Absolute Density Estimates
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Number per unit area
Relative Density Estimates
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Number per unit effort
Catch Per Unit Effort
Catch Per Unit Effort
Catch Per Unit Effort
Nearest Neighbour Estimates
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What if detection changes with
distance?
Transect Sampling
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Density = N / L x 2W
Length (L)
W
W
Hayne’s Estimator
Hayne’s Estimator
White-eared Kob Data (after Krebs 1989)
Line Transect Estimators
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Line Transect Estimators
Line Transect Estimators
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Line Transect Estimators
Line Transect Estimators
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Line Transect Estimators
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Assumptions
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Distance sampling requires that:
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all animals on or near the transect line must be seen,
distances from the transect to the animals are
measured accurately, and
animals are spotted and accurately located before
they move in response to the approaching observer.
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Sightability Models
Advantages
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Each each population estimate requires only one
sample or overflight
Natural movements and double counting are not
a problem
Technique is robust to variable visibility of
animals within and between surveys
Technique, sampling protocols, and statistics
have been extensively developed.
Sightability Models
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Visibility of an animal depends in part on the
habitat is in, group size, the observer, animal
activity, and perhaps even the sex of the animal.
Sightability Models
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Sightability Models: Assumptions
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Groups are sighted independently and that all
meaningful covariates affecting sighting rates
are included in the model
Model development requires an adequate
sample size (100-200 groups)
Technique may not be the best choice for
ungulates in situations where detection rates
are low, especially when detection rates
average less than 50%.
Model developed based on the sightability
rate of marked or ground-truthed animals
Model predicts sighting probability of
individual groups of animals based on a set of
covariates such as group size, percent tree
and shrub cover that will hide animals,
percent snow cover, observer experience,
survey intensity, etc.
The logistic regression model of the sighting
covariates is then applied to the sighting
conditions recorded for each count unit and
each entire survey.
Advantages and disadvantages
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Sightability models are most useful if sighting
rates for all groups are >60%
Models are specific to covariates affecting
sighting rates; hence, different model
variants are required for different aircraft,
different seasons, and different landscapes
Considerable time, cost, and effort goes into
model development and calibration.
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Prairie Habitat Joint Venture
Program
John H. Giudice, John Ratti, E. (Oz) Garton
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Prairie Habitat Joint Venture
Program
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Millions of dollars spent on habitat programs
designed to increase annual duck production.
need reliable data to evaluate program
effectiveness and guide future management
and planning.
Prairie Habitat Joint Venture
Program
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Brood surveys should furnish simple, direct, and
cost-effective data on annual duck production.
Most serious problem with brood surveys is
visibility bias (i.e., the failure to observe all
broods that were present during a survey).
Visibility bias is a major cause of inaccuracy in
wildlife surveys.
Prairie Habitat Joint Venture
Program
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Study Objectives
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identify and quantify the factors that
influence brood visibility;
determine the feasibility of using sightability
models to estimate brood visibility; and
no reliable, timely, and inexpensive methods for
estimating annual production of ducks.
Duck broods are often secretive and difficult to
count.
Need for standardized brood-survey procedures
that incorporate statistical methods of sampling
and sightability correction (sightability models or
mark-resight methods)
Methods
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“We used a modified point-count method and 93
radio-marked mallard broods on 7 PHJV
Assessment sites (1999-2000) to develop
predictive sightability models and assess the
relative importance of sightability covariates.”
design standardized survey procedures that
minimize controllable sources of variation in
brood surveys and are compatible with the
sightability-model methods.
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Results
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Mean visibility of mallard broods was 24%, but
detection rates ranged from 13 to 51%
depending on year and scale of application
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Observer experience (years of survey
experience) and weather (temperature and wind
speed) also influenced detection probability,
although effects were less important than
percent visual obstruction or brood age
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Brood visibility was negatively correlated with
percent visual obstruction and brood age
Results
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Results
Wind speed appeared to be more important than
temperature, especially wind speeds >7 km/h.
Sightability models developed at the brood and
survey-area scale correctly classified 80 and
72% of mallard broods as missed or detected.
Sightability Model other examples
Anderson, Charles R., Jr. and Lindzey, Frederick G. 1996. Moose
sightability model developed from helicopter surveys. Wildl. Soc.
Bull. 24:247-259.
Ayers, Loren W. and Anderson, Stanley H. 1999. An aerial sightability
model for estimating ferruginous hawk population size. J. Wildl.
Manage. 63:85-97.
Samuel, Michael D.; Garton, Edward O.; Schlegel, Michael W., and
Carson, Robert G. 1987. Visibility bias during aerial surveys of elk in
northcentral Idaho. J Wildl Manage. 51:622-630.
Unsworth, James W.; Kuck, Lonn, and Garton, Edward O. 1990. Elk
sightability model validation at the National Bison Range, Montana.
Wildl Soc Bull. 18:113-115.
Overview of Mark-Recapture
Methods
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Estimation of population size of a geographically
and demographically closed but free-ranging
population is a common problem encountered by
biologists.
Overview of Mark-Recapture
Methods
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The earliest approaches to this problem were
developed by Petersen in 1896 and later by
Lincoln in 1930, where capture-recapture
techniques were applied.
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Simple Mark-Recapture Methods
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Lincoln-Peterson Method
Closed populations, single marking — LincolnPetersen method Lincoln (animal), Petersen
(fisheries)
Closed populations, multiple markings —
Schnabel method
Open populations, multiple sampling — JollySeber method.
Lincoln-Peterson Method
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Krebs (1989) provides a succinct method for
estimating confidence intervals.
If a Petersen population estimate has a very
wide confidence interval, you should not place
too much faith in it.
Jolly-Seber Estimator
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Jolly-Seber Estimator
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Jolly-Seber (Jolly 1965) method extends markrecapture to the more biologically realistic
situation of open populations.
Jolly-Seber Estimator
Individuals are marked with tags that are
specific to the sampling period.
When was this marked individual last
captured?
The time interval between samples need not
be constant, and any number of samples can
be accommodated so that series of data
extending over may years can be used with
this method.
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Jolly-Seber Estimator
Program Mark
Program Mark
Program Mark
Program Mark
Program Mark
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Estimation from mark-resighting
surveys
Program MARK
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Program MARK provides parameter estimates from
marked animals when they are re-encountered at a
later time. Re-encounters can be from dead
recoveries (e.g., the animal is harvested), live
recaptures (e.g. the animal is re-trapped or resighted), radio tracking, or from some combination of
these sources of re-encounters. Check out the
description of its capabilities, or information on how
to download the program.
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http://www.cnr.colostate.edu/~gwhite/mark/mark.htm
Estimation from mark-resighting
surveys
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Estimation from mark-resighting
surveys
The mark-resight procedure has been tested
with known populations of mule deer
(Odocoileus hemionus; Bartmann et al. 1987)
and used with white-tailed deer (Rice and
Harder 1977), mountain sheep (Furlow et al.
1981, Neal et al. 1993), black grizzly bear
(Miller et al. 1987), and coyote (Hein 1992).
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Alternative Wild Horse and Burro
Survey Techniques
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http://www.fort.usgs.gov/WildHorsePopulations/AlternativeTech.asp
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USGS Fort Collins Colorado
The initial sample of animals is captured and
marked with radios, but recaptures of these
animals are obtained by observation, not
actually recapturing them.
The limitation of this procedure is that
unmarked animals are not marked on
subsequent occasions.
The advantage of this procedure is that
resightings are generally much cheaper to
acquire than physically capturing and
handling the animals.
Program NOREMARK computes 4 markresight estimators of population abundance,
modeling variation of sighting probabilities
across time, individual heterogeneity of
sighting probabilities, or immigration and
emigration from a fixed study area (Eberhardt
1990).
Alternative Wild Horse and Burro
Survey Techniques
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population estimates drive nearly all management
decisions pertaining to wild horses and burros, accuracy
is important.
Several widely used techniques exist for conducting
aerial population estimates, but they each have
limitations.
evaluating combinations of these techniques in
estimating population numbers of wild horses and
burros.
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Mark-Resight
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Artificial marking devices, such as radio collars,
are considered unacceptable on wild horses.
Mark-Resight
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Simultaneous Double-Count
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A form of mark-resight
Two observers in an aircraft independently observe and
record groups of wild horses or wild burros
Sighting rates are estimated by comparing sighting
records of the two observers
Groups seen by both observers must be identified, either
by communication with a third observer during the flight,
or by matching observations based on time, location,
and other characteristics of the sighting
Simultaneous Double-Count
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Simultaneous Double-Count
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No capture or handling of animals or pre-survey work is
required
Observer differences estimated and accounted for
To ensure that observations are independent
(uncorrelated), aerial observers can be isolated through
the use of barriers and adherence to strict guidelines
and discipline
The variable visibility of different groups of animals is a
bigger challenge; however, can be addressed through
analyses
estimate precision can be improved by “marking” or
photographing a large portion of the population during
the first survey.
cost of marking (sighting once) is no higher than for
resight: allocating roughly equal effort to the sighting
and resighting surveys should produce the most costeffective estimate.
Those animals seen by the one observer are the
“marked” groups; those that are also seen by
the other observer are “resighted.”
Sighting probabilities for both observers can be
computed from this information
Standard mark-resight or Lincoln-Petersen
calculations are used to generate a population
estimate.
Sightability Bias Correction Model
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The model must hold over space, time, and new
observers for estimates to be valid, and populations
within each count unit must remain constant during the
survey.
accounting for multiple sighting factors is also the
sightability model’s chief advantage.
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Distance Sampling
Distance Sampling
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Two observers located on either side of an aircraft
record the size of all groups seen and the perpendicular
distances from the transect line to each group
Transect lines must be placed randomly (or
systematically with a random start) but do not
necessarily have to be straight; contour lines can be
flown instead
Location of and distances from the transect line can be
measured using GPS and other technologies.
Combining Techniques
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The combination of multiple sources of information
overcomes most of the deficiencies of the separate
techniques and provides greater power and efficiency
For example, the major difficulty in the double-count
technique—ensuring similar sighting probabilities for all
animals—can be resolved by modeling sightability using
covariates in a manner similar to the sightability bias
correction model
The biggest challenge is likely to be movement
of wild horses in response to the approaching
aircraft prior to detection by observers.
Combining Techniques
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No pre-calibration of the model is required, and the
assumption that the initial calibration applies uniformly
over space, time, and observers is eliminated.
Similarly, the requirement in distance sampling that all
animals near the transect line are spotted can be
eliminated by applying data from a double-count to
estimate the detection probability on the line
Both the mark-resight and distance sampling methods
can be made more precise by incorporating sightability
covariates.
General References
General References
Jolly, G.M. 1965. Explicit estimates from capture-recapture data with
both death and dilution — stochasitc model. Biometrika 52:225247.
Seber, G.A.F. 1982. The estimation of animal abundance and related
parameters, 2nd ed. Griffin, London.
White, Gary C. 1996. NOREMARK: Population estimation from markresighting surveys. Wildlife Society Bulletin. 24:50-52.
Krebs, C.J.1989. Ecological Methodology. Harper and Row, New York.
Otis, David L.; Burnham, Kenneth P.; White, Gary C., and Anderson,
David R. Statistical inference from capture data on closed animal
populations. Wildlife Monographs. 1978; 62:1-135.
Schnabel, Z.E. 1938. The estimation of the total fish population of a
lake. Am. Math. Month. 45:348-352.
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